Relativity and Empiricism

[Erasmus00]

Rather then drag this this thread off topic, I wanted to pose some questions for Hilton Ratcliffe here. To start:

 

Given the phenomenal success of theories special relativity based theories (such as QED,QCD,electroweak), how can we doubt that special relativity wasn't on to something?

 

In other words, you wish to work with a euclidean 3 dimensional universe with an absolute time parameterizing trajectories. However, the best tested theories we have are not mappable to this model (i.e. quantum field theories). How can we hold to Euclid in light of this? How can we ignore Minkowski?

-Will

[Hilton Ratcliffe]

Hi Will,

 

Thank you for your questions. My criticism of Relativity and the Gaussian geometry from which it was eventually drawn is confined to the phenomenological universe in which I work. I understand that for entities beyond the scale of direct observation and measurement, we have no choice but to try to imagine how things might be, and I concede that the only way to do that with any relevance is by mathematics. Any discussion of those areas of enquiry are limited to mathematical debate, and that in itself can lead to a maelstrom of ideas that conclude themselves only to those individuals suitably fluent in the mathematical syntax being employed. I distance myself from such enquiry, because I find (probably as a result of my own ignorance) that it is simply frustrating and almost impossibly hard to verify in many cases.

 

However in the observed universe that astronomers deal with, we are not compelled to resort to meta-mathematical abstractions. It is a universe that obviously exists in 3-D Euclidean space, and therefore I maintain that we should not treat it in any other way if we want real answers to our problems of measurement. Without any hard data to back up my contention, I believe that a mechanical link will eventually emerge between macro and micro, or at the very least, we will discover that we don't need completely different, often irrational, physics to describe anything in the physical universe. It my view that we have arrived at these successful but unilateral models of sub-atomic phenomena precisely because of the mathematical route that has become standard in science. As soon as one removes the neccessary restraint of our common reality, one is given dangerous and consuming freedom to re-define reality to suit one's equations.

 

Best regards

Hilton

[Qfwfq]

As soon as one removes the neccessary restraint of our common reality, one is given dangerous and consuming freedom to re-define reality to suit one's equations.

So Maxwell, Lorentz and Einstein wrote their equations arbitrarily and the results of all experiments of electricity, magnetism and optics were bent to suite those equations... :phones:

[modest]

Is the suggestion that we go back to æther and a variable speed of light, or that we accept the validity of SR and GR but try and put them into Euclidian geomatry?

[Pyrotex]

Hi Will,...However in the observed universe that astronomers deal with, we are not compelled to resort to meta-mathematical abstractions. It is a universe that obviously exists in 3-D Euclidean space,...

Given the first question in this thread, it is not clear what aspects of mathematical modeling you are objecting to. By inference from other posts, you are claiming that Special Relativity (at least) is unnecessary. Maybe even General Relativity. You also appear to be saying that there are no observational reasons for concluding that Einstein's math explains the real 3-D universe.

 

Au contraire, mon ami. The observational evidence for both Relativities is vast and plentiful. Especially from astronomy.

[Hilton Ratcliffe]

Hi Modest,

 

Is the suggestion that we go back to æther and a variable speed of light, or that we accept the validity of SR and GR but try and put them into Euclidian geomatry?

 

I live and breathe in a 3-D Euclidean universe. My suggestion is therefore that we form our theories of things that happen in this universe using the appropriate geometry. In essence, I am saying that Einstein's Relativity attempts to fix something that isn't broken, at least not in the observed and measured universe.

 

Best

Hilton

[Qfwfq]

A farmer in Holland who never travels or rises above the ground lives and breaths on a very flat piece of land, surrounded by other very flat pieces of land. When working out shapes and measures of these fields and their boundaries, for purchasing them or for splitting them between heirs, it is perfectly appropriate to use good ol' Euclid's geometry.

 

And 2-D, to boot.

[modest]

Hi Modest,

 

 

 

I live and breathe in a 3-D Euclidean universe. My suggestion is therefore that we form our theories of things that happen in this universe using the appropriate geometry. In essence, I am saying that Einstein's Relativity attempts to fix something that isn't broken, at least not in the observed and measured universe.

 

Best

Hilton

 

Is there something I don’t know about Euclidean geometry that makes it more "appropriate" to other geometries - perhaps that it was described first? Is a spherical surface better in some fundamental way than a hyperbolic surface?

 

GR can be described with a 3-dimensional hypersphere embedded in a 4-dimensional Euclidean space with an imaginary time coordinate or a 4-dimensional hyper-hyperboloid in a 4+1-dimensional Minkowski space-time. (1) To me, these seem like different descriptions of the same thing. I don’t believe an idea or a model should be arbitrarily dismissed because of the coordinate system used to describe it. As we know, these models of SR and GR can be described in more than one geometry. I believe this is a product of geometry or more essentially math, and not the reality or validity of the model itself.

 

Or, should we limit ourselves to only using Euclidean geometry when describing physics? How would this help in our understanding the universe?

 

-modest

[Hilton Ratcliffe]

Hi Modest,

 

Or, should we limit ourselves to only using Euclidean geometry when describing physics? How would this help in our understanding the universe?

 

Don't you agree that in the area of investigation described in my earlier posts, Euclidean geometry is the simplest, easiest and most accessible way of quantitatively describing the environment? Furthermore, do you not agree that it is a system of directly mapping observed phenomena in the way that we empirically conceive of it? It does not need convoluted mathematical expression. That would make it fundamentally better, in my opinion, unless the relativistic method gives us answers that we cannot obtain by this method. If you disagree, then I fear we have reached an impasse where we are both excercising our choice of first principles, and simply seeing it differently. I assume a 3-D Euclidean universe because it is the one I see.

 

Best

Hilton

[sanctus]

Are you sure it is the one you see? When you look at stars for example their position can be shifted by gravitational lensing for example. Or what about the perihelium of Mercury (don't know if this is the good translation into english of what I mean, ask in case it isn't)?

 

Your argumentation seems a bit middle-agish in the sense that the motivation is: "because it is the one I see" just as all the non-scientifics from inquisition argued geocentrism...

[Hilton Ratcliffe]

Hi Sanctus,

 

I'm sorry, I did not express myself well. What I meant was that the geometry of the universe we see is obviously Euclidean. Relativity as a relationship between objects in motion is not solely the province of Einstein. Classical mechanical relativity, as I'm sure you know, predated Einstein's version by hundreds of years. Of course we do need to take relativity into account. I don't see the need or the advantage of using non-Euclidean geometry. Other aspects of observation like aparent motion, the bending of light near massive objects, and so on, have classical explanations as well as relativistic ones. Both systems produce isolated anomalous results and exceptions to the rule, and both have a wealth of observational support. It would seem that the choice, if we have one, is a matter of personal preference. Neither description is sacrosanct.

 

Newtonian mechanics needs to be developed as we go along. In particular, the area of n-body gravitation is fertile ground for research. Also, it seems we need to include other forces of nature in certain cases, as in the rotation of galaxies and clusters. Merely inserting a balancing term into the equations is to me an unsatisfactory way of doing it, although for purely practical reasons I do use MOND.

 

Best

Hilton

[modest]

Hi Modest,

Don't you agree that in the area of investigation described in my earlier posts, Euclidean geometry is the simplest, easiest and most accessible way of quantitatively describing the environment? Furthermore, do you not agree that it is a system of directly mapping observed phenomena in the way that we empirically conceive of it? It does not need convoluted mathematical expression. That would make it fundamentally better, in my opinion, unless the relativistic method gives us answers that we cannot obtain by this method. If you disagree, then I fear we have reached an impasse where we are both excercising our choice of first principles, and simply seeing it differently. I assume a 3-D Euclidean universe because it is the one I see.

 

Best

Hilton

 

I guess I don’t accept your premise that a Euclidean coordinate system is more real because it is more-often simple. In fact, it could be argued that Minkowskian geometry has time and so is more-correct to our every-day experiences. A coordinate system containing gravity would be even more-correct to our every day experiences. But I would hold off on saying any geometry is an accurate description to our universe. They are all just using math to give us coordinates matching things we see and predict. A 2-D map of the earth isn’t wrong, it is just sometimes more convenient than a globe. Euclidian isn’t wrong it is just often more convenient. And Minkowskian is sometimes more convenient and often more complete. None of them are wrong and to an extent they are all accurate.

 

It’s an interesting idea, however, to try and disprove a model by attacking the geometry that best describes it. But, I think to do that you would have to make a proof against the math or method of creating the coordinate system. Even if that could be done, these theories can be described using different geometries - so it seems like a loosing battle.

 

Besides, special relativity was created with euclidean geometry. It wasn't until later that people created other geometries to describe it as a function of space-time. So, how can your problem with special relativity be one of geometry? Or, is your problem with SR itself? If so, why the hell are we talking about geometry :evil: :thumbs_up

[Qfwfq]

Let's try to sort a few things out here folks:

 

Classical mechanical relativity, as I'm sure you know, predated Einstein's version by hundreds of years. Of course we do need to take relativity into account.

You presumably refer to Galileo having first stated the principle of relativity in his dialogue, and Newton giving it as corollary VI after the three axioms. Theory of Relativity is simply what Einstein's publication "Zur Elektrodynamik Bewegter Körper" came to be known as; the reason is that it solved the apparent incompatibility between electromagnetism and the Sacred Principle. It definitely is a misconception that Einstein was the first to state it. Unfortunately, names stick and they can often cause confusion.

 

Other aspects of observation like aparent motion, the bending of light near massive objects, and so on, have classical explanations as well as relativistic ones.

Lot's of folks have worked out the differences in predictions.

 

Newtonian mechanics needs to be developed as we go along.

Absolutely. Indeed Minkowski did so by formulating SR in terms of Newton's three axioms, albeit using 4-vectors and derivation by proper time rather than by the t coordinate.

 

In fact, it could be argued that Minkowskian geometry has time and so is more-correct to our every-day experiences.

Er... the idea of time as a fourth geometric dimension isn't strictly confined to Minkowskian geometry. The real difference is in the coordinate transformations, of which the Lorentz ones follow naturally from Minkowski's metric.

 

A 2-D map of the earth isn’t wrong, it is just sometimes more convenient than a globe.

Er... the globe's surface is also a 2-D manifold; not a flat one, but nonetheless a 2-D manifold. To a farmer in Holland, the fields are quite flat. To anyone that can see a larger extent at a time, it becomes obvious that it isn't perfectly flat.

 

How big is your triangle?

[Buffy]

How big is your triangle?

So big that the vertices touch! :(

 

Just to be really painfully clear: the problem really just boils down to the fact that Euclidean Geometry will start to diverge from the more accurate Relativistic Geometry under circumstances that cannot always be predicted (or easily forgotten, or worse, intentionally misused). As a result, uncritically relying on Euclidean math will sometimes produce incorrect results, especially when dealing with observations over great distances as sanctus points out.

 

A standard deviation here, a standard deviation there, and pretty soon you're talking about real error,

Buffy

[modest]

 

In fact, it could be argued that Minkowskian geometry has time and so is more-correct to our every-day experiences.

 

Er... the idea of time as a fourth geometric dimension isn't strictly confined to Minkowskian geometry. The real difference is in the coordinate transformations, of which the Lorentz ones follow naturally from Minkowski's metric.

Thank you for expanding on what I was saying - this is my thinking exactly

 

They are all just using math to give us coordinates matching things we see and predict. A 2-D map of the earth isn’t wrong, it is just sometimes more convenient than a globe.

 

Er... the globe's surface is also a 2-D manifold; not a flat one, but nonetheless a 2-D manifold. To a farmer in Holland, the fields are quite flat. To anyone that can see a larger extent at a time, it becomes obvious that it isn't perfectly flat.

 

Well, I was thinking more along the lines of the map being square and stretched and thus less accurate. Have you seen how big Greenland looks? :(

I suppose an argument could be made for most globes having bumps and ridges for mountain ranges and therefore being 3-D. Probably not the best measure of altitude though :)

 

-modest

[Turtle]

Well, I was thinking more along the lines of the map being square and stretched and thus less accurate. Have you seen how big Greenland looks? :confused:

 

The accuracy -and the features that accuracy refers to- is dependant on the type of projection used. The common world map wherin Greenland looks huge is often a Mercator projection. Buckminster Fuller invented the most accurate flat-map projection of the Earth, called a Dymaxion Projection.

 

Here's a general article on the many different >> map projections.

 

I suppose an argument could be made for most globes having bumps and ridges for mountain ranges and therefore being 3-D. Probably not the best measure of altitude though

 

-modest

 

No; not so much. :eek2: :angel:

[Hilton Ratcliffe]

Hi all,

 

Modest said:

It’s an interesting idea, however, to try and disprove a model by attacking the geometry that best describes it.

Besides, special relativity was created with euclidean geometry. It wasn't until later that people created other geometries to describe it as a function of space-time. So, how can your problem with special relativity be one of geometry? Or, is your problem with SR itself? If so, why the hell are we talking about geometry

I can see how the impression has been created that I am attacking something. This is a misconception, and I am guilty of encouraging it. Often, this type of dialogue morphs from enquiry seeking answers to an attack-and-defence conflict seeking an ultimate victor. My position is this: I am an astrophysicist practicing his craft without involving Einstein’s relativity, and as far as I am aware, have suffered no ill effects because of this (other than scorn and derision!:confused:). On the contrary, it seems to have made my life easier. However, most of my colleagues choose do their science the standard way, and I am not so stupid as to deny the possibility—probability even—that somewhere my chosen path is producing the wrong answers. Hence my asking of the question, “Is Newtonian Mechanics an advantage or a limitation in astrophysics?” To avoid degenerating this discussion to an argument over definitions—I can immediately see that we seem to define Euclidean geometry differently—may I suggest reference to the other thread? That will give my understanding of Newtonian Mechanics, classical physics, and classical relativity without my having to repeat all that here. I’m hoping that will answer your question about why we are discussing geometry in a discussion about Relativity and Empiricism.

 

Buffy said:

Just to be really painfully clear: the problem really just boils down to the fact that Euclidean Geometry will start to diverge from the more accurate Relativistic Geometry under circumstances that cannot always be predicted (or easily forgotten, or worse, intentionally misused). As a result, uncritically relying on Euclidean math will sometimes produce incorrect results, especially when dealing with observations over great distances as sanctus points out.

 

Buffy, I think you may here have made a promising suggestion why I am wrong to ignore Relativity. It seems Euclidean maths may produce anomalies at extremes of measurement, not only distance, but also speed and under strong gravitational regimes. Unfortunately GR has not been tested at those extremes (has it?) and in attempting what Coldcreation suggested elsewhere, viz setting boundaries of applicability for NM and GR, we may run into a logical obstacle: GR and SR apply to the exclusion of NM in a very remote place, but have only been tested locally. Dr Subrahmanyan Chandrasekhar responded as follows to a lecture by Paul Dirac in which he (Dirac) claimed that Einstein’s theory of gravitation was eminently successful:

“It does not seem to me that the successes of Einstein’s theory are either long or impressive…[]…all these relate to departures from Newtonian theory by a few parts in a million; and of no more than three or four parameters in a post-Newtonian expansion of Einstein’s field equations. And so far, no predictions of general relativity in the limit of strong gravitational fields have received any confirmation; nor are they likely in the foreseeable future.” (S. Chandrasekhar Relativistic Astrophysics Collected Papers: S. Chandrasekhar Vol. 5, University of Chicago Press, 1990).

 

Best

Hilton